Can I set the rendered viewport to be a lower resolution on a high resolution monitor?
Not at the moment I'm afraid. Until recently such high resolution screens were uncommon, and it was rarely a problem.

With the advent of high DPI displays, UHD resolutions and 5K monitors the resulting pixel dimensions of a viewport are becoming a more common issue for live rendered preview, since it requires a lot of resources to render at such potentially high resolutions.

There are plans to support this in the future, and upcoming versions of Blender 2.8 already address the issue.

As stated in the wiki release notes page, introduced by commit 66c1b23aa10d there is now a viewport performance setting called Pixel Size which allows setting a scaling factor for the rendered viewport previews to a different resolution, to keep responsiveness at acceptable levels.

For the time being, in stable version of Blender the only workarounds are to either use Render Border to render a subsection of the canvas; or when inside a camera view, zoom it out in the 3D view, so the effective camera frame is smaller on screen resulting in less area to render.